What is the upper limit of cake pan size before I definitely need a tube cake pan of angel food cake?

The answer, like most other things in life, is: "it depends". Angel food cake (and chiffon) can be very sensitive air pressure and humidity. You will find that on rainy days, the cake will rise higher and therefore have more of a tendency to collapse on you after baking. There really isn't a hard upper limit on when you'll need to use a tube pan.

That said, you might be able to get away with a 7-inch angel food cake if you do it at a low enough temperature and you're careful not to try baking it on a rainy day. You probably wouldn't get away with that using a 9-inch pan on any day, though. All you can do is try it and see what happens.